BOB SCHIEFFER: Today on FACE THE NATION, the whacky week in Republican politics.

HERMAN CAIN (R-Presidential Candidate): There are factions that are trying to destroy me personally as well as this campaign.

BOB SCHIEFFER: While Herman Cain spent the week on national television denying allegations of sexual harassment, the internet and late night comics were all abuzz about a bizarre-o speech that Rick Perry made in New Hampshire.

RICK PERRY (R-Presidential Candidate): This is such a cool state, I mean come on, live free or die? I mean, you know, you got to love that right?

BOB SCHIEFFER: What is going on? Who's been helped? Who was hurt? We'll talk about it with a cross section of Republicans, Rick Perry campaign supporter Ken Blackwell, former Bachmann campaign manager Ed Rollins, the former head of the Republican Party Ed Gillespie and activist and strategist Liz Cheney. We'll round it out with CBS News political analyst John Dickerson. Then we'll meet the young women behind another video that's gone viral, three of Jon Huntsman's daughters, Abby, Mary Anne and Liddy.

It's all ahead on FACE THE NATION.

ANNOUNCER: From CBS News in Washington, FACE THE NATION with Bob Schieffer.

BOB SCHIEFFER: And we have Republicans all across the country prepared to speak this morning and we are ready to poll the delegation. The first thing we're going to talk about is this week that Herman Cain had here in Washington. Charges of sexual harassment were raised against him and at one point, it was just every stop he would either add or change the story and talk about what had happened. I want to just play you just a brief clip of his day here-- or his week in Washington.

HERMAN CAIN: I have never sexually harassed anyone. It is totally baseless and totally false.

I do remember the formal allegation she made in terms of sexual harassment.

As far as a settlement, I am unaware of any sort of settlement.

I was aware that an agreement was reached.

I got out in front and was direct in addressing this issue.

BOB SCHIEFFER: So, Ed Gillespie you were the head of the Republican Party at one point. You've been a strategist in many campaigns over the years. The Cain people keep saying end of story. Is it the end of the story?

ED GILLESPIE (Former Republican National Committee Chair): Well, I don't know if it's the end of the story. And obviously any time you're talking about sexual harassment instead of your tax reform plan you're not on the message you want to be on. I do think though, that a lot of Republican voters think that, you know, when there's an anonymous, you know, allegation that there's a-- there's a sense amongst many Republicans that there's a, you know, that's not exactly fair. Two, I think the conservatives believe that liberals, you know, have kind of a special disdain for black conservatives and-- and I think that they feel that there's an unfairness that's at-- at play here. And so I think that actually, you know, this is not as damaging to Herman Cain. The third thing I would say is that, you know, he is an unconventional candidate, but it's an unconventional year. His respon-- response has been unconventional. But I think one of the things you're seeing, at least you're not seeing yet, is as much damage as you would expect in other years or with other campaigns.

BOB SCHIEFFER: Well, you're right on that because the only poll we have since all this began was in the Washington Post. It showed that his support had not lessened at all. But as for liberals being behind it, he was saying at one point this week it was not liberals but the Perry campaign that had leaked this information. Ed Rollins, what do you think he has to do now? Has he been hurt by all of this even though the polls show he's generally holding the support he had?

ED ROLLINS (Former Bachmann Campaign Manager): Well, first of all you got-- sometimes it takes two or three weeks for polls-- for these incidents to really show up in polls. In this segment of the electorate that he has, this twenty-five percent-- you know, there's been seven people who have been front-runners in this campaign since the beginning. And most of them have had that same twenty-five, thirty percent that he's had, everybody from Trump to Bachmann to Perry to-- to and now to Cain. So I think that vote will move back and forth a little bit until it solidified. He's not out of this yet. He can't basically say I'm not going to answer any more questions on this. As fask-- facts come forward even though it's an unconventional campaign with an unconventional candidate, Republicans want to win. We want basically a candidate who can go up against Obama and beat him and we think we have got an excellent opportunity for that. So this is a--there's a year to go. There's less than sixty days to go before the Iowa caucuses, so a week is a lifetime in politics. A month is even more so and a year is an eternity. So I think you're going to see a lot of things happening and I think that Herman has not basically either answered the questions correctly or has seen the last of this.

BOB SCHIEFFER: Well to that point, that now seems to be the new strategy. Last night, he-- he came down pretty hard on that. Listen to what he said last night when somebody tried to ask him.

WOMAN: Mister Cain the attorney for one of the women who filed a sexual harassment complaint against you--